Dynamics and number theory long were quite dinstinct fields of mathematics. Recently, however, progress has been made in the application of number theory to dynamics. This text seeks to elucidate a...Show moreDynamics and number theory long were quite dinstinct fields of mathematics. Recently, however, progress has been made in the application of number theory to dynamics. This text seeks to elucidate a small bit of this progress. The focus will be on the special case of discrete dynamical systems, which consist of a set X associated with a map φ : X → X. As in this text we will mainly consider X = P n (Q), the first section serves as an introduction to projective geometry. To provide the reader with some intuition, it starts out with P 1 (C) and eventually switches attention to P n (Q). The second section introduces the basic notions of discrete dynamics. In the third section, ‘height functions’ are defined. These are functions of the form h : P n (Q) → R, and they serve as the main tool in applying number theory to dynamics. As we restrict attention to projective spaces over Q, their definitions can remain quite simple; when working over an arbitrary number field K, one runs into the problem that the ring of integers of K may not be a principal ideal domain, making the definition of h substantially more complicated. For this, refer to [1]. After having defined them, some important properties of the height functions are derived. Section 4 then utilizes these properties to quickly derive some interesting theorems relating arithmetic to discrete dynamical systems.Show less
In 2003 Arjen Doelman and Tasso J. Kaper published an article named Semistrong Pulse Interactions in a Class of Coupled Reaction-Diffusion Equations. In this article blow-up behavior was found in...Show moreIn 2003 Arjen Doelman and Tasso J. Kaper published an article named Semistrong Pulse Interactions in a Class of Coupled Reaction-Diffusion Equations. In this article blow-up behavior was found in simulations of two modified Gierer-Meinhardt systems. In this thesis this behavior in both of these systems is analyzed. First we will use rescalings to construct explicit first order expressions for the blow-up solutions. These theoretical results are illustrated by simulations.Show less
This thesis concerns a low-tech fabric analysis on two types of fabrics found in Dutch archaeological context. This early-medieval pottery has been made in the German Rhine valley, close to Cologne...Show moreThis thesis concerns a low-tech fabric analysis on two types of fabrics found in Dutch archaeological context. This early-medieval pottery has been made in the German Rhine valley, close to Cologne, called „Vorgebirge‟. In this region, several potteries produced pottery with the same raw materials, which makes it hard to know their provenance. Two small villages, Badorf and Walberberg, are known to have produced a lot of pottery. The fabrics of these typical pots are light-coloured, mostly tempered with fine sand and baked at high temperatures. The produced forms are for instance relief-band amphorae, large vessels and cooking pots, but smaller forms also occur. The pottery was exported and traded by river (Rhine, lower Rhine, Meuse, IJssel) to early-medieval settlements in the lower countries and from there exported overseas. In Dutch archaeology, this typical pottery has been found at large-scale trade centres like Dorestad, but also on small sites related to big trade routes. The large quantity of sherds archaeologically found at Dorestad has been used to make a typology based on forms and fabrics. This typology is still used as a reference in processing sherds. The problem is that these sherds are examined on characteristics like colour and hardness, but those are problematic because of factors like baking atmosphere and post-deposition. However, with the low-tech fabric analysis it is possible to get a better notion in these fabrics. In this method a sample of a sherd is used, to get a fresh break. After preparation, this sample is re-baked at 900 °C to get disposed of sample-differences like moistness and to be able to reconstruct the original firing of the pots. Afterwards, the fresh breaks of these samples are all microscopically tested on several factors like calcite, colour and hardness subsequently, and their fabrics are described on porosity by looking at pores as well as on the main tempering and texture. By doing this, a distinction between the fabrics and a comparison with the results with other analyses can be made. The present low-tech fabric analysis on the Walberberg and Badorf fabrics sets a clear example of how useful this method is. It clarifies that several specified sherds should be determined differently.Show less
In Guyana wordt een bepaald soort sjamanisme toegepast. Deze vorm van sjamanisme heeft als kenmerk dat hij samengaat met veel geweld. De sjamaan (in de plaatselijke taal Kanaima genoemd)...Show moreIn Guyana wordt een bepaald soort sjamanisme toegepast. Deze vorm van sjamanisme heeft als kenmerk dat hij samengaat met veel geweld. De sjamaan (in de plaatselijke taal Kanaima genoemd) achtervolgt het slachtoffer om hem of haar na een bepaalde tijd ritueel te doden. Om er achter te komen wat er allemaal komt kijken bij dit soort gedrag, moeten we ingaan op een aantal psychologische kenmerken. Aan de hand van vijf onderwerpen (te weten morele overweging, sociale motivatie, het doelwit, de uitvoerende en de herkomst van de magische kracht) wordt een beeld geschetst van deze vorm van sjamanisme. Het model wordt ten eerste toegepast op twee relevante studies ter vergelijking. Hierdoor kunnen we het model in werking zien. Hierna wordt het model toegepast op Kanaima. Als laatste worden de verschillen en overeenkomsten tussen Kanaima en de twee andere studies naast elkaar gehouden om eventuele blinde vlekken in te vullen die bij zullen dragen aan beantwoording van de vragen “ Wat is Kanaima?”, “Wie is Kanaima” en “Waarom bestaat Kanaima?”.Show less
This thesis is about an early medieval well, made of sods, from a Roman and medieval site in Naaldwijk, Zuid-Holland, the Netherlands. All the wood from this well, including part of a wooden wheel,...Show moreThis thesis is about an early medieval well, made of sods, from a Roman and medieval site in Naaldwijk, Zuid-Holland, the Netherlands. All the wood from this well, including part of a wooden wheel, was examined together with soil samples, one from the bottom filling of the well and one from the sods, for the presence of seeds. The main research question was: “How did the local vegetation look like at the time of the well, based on the examined wood and seeds?” A second complementary question was: “What was the character of the use of wood?” In the well wood of alder, oak, ash, willow, buckthorn and elder was found, possibly all of these have grown in the area near the settlement. Most of the found wood was of poor quality and together with the findings of branches of most of the taxa suggest the use of local wood and therefore the availability was the main factor in the choice of wood. Research of the seeds from the soil sample that was taken from the sods showed that the sods probably came from a clayey environment that given the amount of foraminifera in the sample, has possibly been under the influence of the sea. The discovered taxa in this sample seem to indicate a moist to wet, moderately brackish to brackish environment. The soil sample from the bottom filling of the well showed many arable weeds that seem to indicate the presence of lime-free, nitrogen-rich and moderate to rich farmland or vegetable gardens. There are indications for frequently entered environments with a rich soil, such as yards and roadsides. Also ample evidence was found of rarely entered brushwood with a reworked rich, humous, lime-free, dry soil, such as waste land and pastures. Some of these taxa are indicators for nitrogen and also occur in fields and can point to manuring of the soil. There are also many indications for the presence of grasslands and/ or pastures with a highly variable humidity and a moderately brackish to brackish soil, such as dune grasslands. However, determining the presence or absence of forests and the degree of openness of the landscape can only be done with additional pollen analysis.Show less
De opgraving Brandwijk- het Kerkhof is uitgevoerd 1991 door M Verbruggen en is onderdeel van het donkenproject in de Alblasserwaard. In deze scriptie zijn de werktuigen van been en gewei, afkomstig...Show moreDe opgraving Brandwijk- het Kerkhof is uitgevoerd 1991 door M Verbruggen en is onderdeel van het donkenproject in de Alblasserwaard. In deze scriptie zijn de werktuigen van been en gewei, afkomstig van deze opgraving, microscopisch bekeken op zoek naar gebruikssporen. De resultaten zijn vervolgens vergeleken met de opgravingen Hardinxveld-Giessendam Polderweg en de Bruin, Schipluiden en Ypenburg. De belangrijkste vondsten van de site Polderweg stammen uit het Laat-Mesolithicum, de Bruin valt net als Brandwijk onder de Swifterbant-cultuur, Schipluiden en Ypenburg stammen uit het Midden-Neolithicum en worden gerekend tot de Hazendonk-groep. Op de site Brandwijk zijn 10 werktuigen, 3 mogelijk werktuig en 2 stukken productieafval gevonden van bot en gewei. De werktuigen zijn opgedeeld in 3 priemen, 3 platte priemen of spatels, en 4 beitels. De werktuigen lijken, zover microscopisch zichtbaar, voornamelijk gebruikt te zijn op plantaardige materialen zoals, gras, bast, twijgen en hout. Werktuigen voor het bewerken van huiden en grote bijlen voor het bewerken van hout zijn niet gevonden op deze opgraving in tegenstelling tot de andere opgravingen. Dit zou kunnen duiden op een seizoensmatige bewoning met specifieke activiteiten maar hier kunnen geen harde uitspraken over gedaan worden zolang het vuursteen materiaal nog niet functioneel onderzocht is. De belangrijkste bewerkingstechniek in deze periode is de metapodiumtechniek. Deze techniek word van het mesolithicum tot ver in het neolithicum gebruikt. Ook op de site Brandwijk is gebruik gemaakt van deze techniek. Echter is er vaker gekozen voor een vergelijkbare techniek waarbij andere langbeenderen gebruikt worden in plaats van de metapodia. Dit kan wijzen op een schaarste aan grondstoffen of een andere voorkeur van de maker. Bij de keuze van gewei is er overeenstemming met de ander opgravingen, er zijn voornamelijk afgeworpen geweien gebruikt. Alleen bij Ypenburg is dit niet het geval.Show less
Martiality, elites and burials are important topics in current Bronze Age studies. Instead of swords, spears and axes, this thesis focuses on Bronze Age archery, and examines one of the most...Show moreMartiality, elites and burials are important topics in current Bronze Age studies. Instead of swords, spears and axes, this thesis focuses on Bronze Age archery, and examines one of the most durable material components of this practice: bronze arrowheads. Despite its durability, only 25 arrowheads make up the entire corpus of bronze arrowheads found in the Netherlands. All except one of those was found in burial mounds. This raises the question of how these objects were usually employed outside a funerary context. This thesis tries to move towards an answer to this question by first collecting and interpreting the knowledge on bronze age arrowheads, putting these objects in a wider framework. It then introduces some theories on the use of bows during the Bronze Age. Functional analysis was applied to the arrowheads of Hijken, Geldermalsen-Eigenblok and Sleen. This lead to some conclusions on the production and use of these objects. It appeared they were cast, and not cut out of sheet bronze, and after slight hammering were polished. No convincing traces of use were found. This, together with the data on the context of the arrowheads, lead to the conclusion that these objects were indeed weapons, and shared their function, efficient implements of killing as well as objects for show, with other weapons.Show less
Uit diverse opgravingen komen cosmeticadoosjes in de vorm van een eend aan het licht. Dit soort doosjes of bakjes worden over het algemeen gedateerd in de bronstijd en gesitueerd in het mediterrane...Show moreUit diverse opgravingen komen cosmeticadoosjes in de vorm van een eend aan het licht. Dit soort doosjes of bakjes worden over het algemeen gedateerd in de bronstijd en gesitueerd in het mediterrane gebied. Over de achtergrond van deze eenden is veel te vertellen maar tegelijkertijd veel onduidelijk. In dit essay onderzoek ik onder andere de herkomst van de zogenaamde “cosmetica eend”. Daartoe behandel ik enkele sites die als voorbeeld genomen kunnen worden. De sites die ik bespreek vertegenwoordigen diverse culturen en typen eenden. Hiermee schets ik een beeld rondom de objecten waarbij de materiaalkeuze centraal staat.Show less
